In chemistry, there are gases that we use every now and often. These gases are governed by something called the “Gas Laws”. From the smallest of laboratory experiments all the way to the vast field of environmental studies, Gas laws are the cornerstone into understanding the behavior of gases in different situations. Gas laws play a crucial role in that field of chemistry. In this article, we shall delve into the world of gas laws. All the way from the fundamental principles that govern them to the various modern applications that we use.

There are primarily three gas laws, Boyle’s Law, Charles’s Law, and Avogadro’s Law. These three laws each have their own conditions for usage. They also work hand in hand to help explain the behavior of gases in different situations. Let us take a deep dive into each one of these laws.

## Boyle’s Law

During the 17^{th} century, a scientist by the name of Robert Boyle pioneered chemistry. He laid the foundation for understanding the relationship between pressure and volume. This inverse relationship is what we now call Boyle’s Law. This law has many applications, from the expansion of our lungs when breathing, in a medical application all the way to the compression of gases in many industrial processes. These are but only a few examples, Boyle’s Law finds practical uses in many other fields.

Boyle’s Law applies to a given gas kept at a constant temperature. The pressure will always be inversely proportional to the volume. When two different gases are under constant temperature, the relationship between their pressure and volume can be expressed in the formula below:

$$

P_1 V_1=P_2 V_2

$$

### Example problem

Let’s Solve a brief problem regarding Boyle’s Law. At a constant temperature, A gas occupies a volume of 400mL at a pressure of 800mmHg. When the volume of the gas is decreased to 200mL, What will the new pressure of the gas be?

#### Solution:

Using Boyle’s Law, we can determine the values that are given.

P_{1} = 800mmHG

V_{1} = 400mL

P_{2} = ?

V_{2} = 200mL

By the formula, we are meant to find the value of P2 or the new pressure of the gas. When the formula is rearranged to:

$$

\begin{aligned}

& P_2=\frac{800 \mathrm{mmHg} \cdot 400 \mathrm{~mL}}{200 \mathrm{~mL}} \\

& P_2=\frac{320000}{200} \mathrm{mmHg} \\

& P_2=1600 \mathrm{mmHg}

\end{aligned}

$$

Therefore, The new pressure of the gas after a decrease in volume will be 1600mmHG.

## Charles’s Law

Charles’s Law is named after Jacques Charles. It explores the direct correlation between temperature and volume. This historic discovery made by Jacques Charles is also one of those very important discoveries that lead to many crucial advancements that we now know today. Advancements were made in aviation, cryogenics, and air conditions to name but a few.

Charles’s Law states that the volume of a given gas is directly proportional to its temperature. But this can only be applied at a constant pressure. The relationship between the volume and temperature of two given gasses at constant pressure can be expressed using the formula below:

$$

\frac{V_1}{T_1}=\frac{V_2}{T_2}

$$

### Example problem

Using Charles’s Law, lets solve a problem. When a sample of gas is kept at a constant pressure. Its initial temperature is 273K when occupying a volume of 2L. If the temperature was to be increased to 373K, what will be the new volume of the sample of gas?

#### Solution

Using Charles’s Law, Lets solve the problem above.

T_{1} = 273K

V_{1} = 2L

T_{2} = 373K

V_{2} = ?

Using the givens above, we can rearrange the Charles’s Law formula to solve for V2 or the new volume of the gas.

$$

\begin{aligned}

& V_2=\frac{(2.00 \mathrm{~L}) \cdot(373 \mathrm{~K})}{273 \mathrm{~K}} \\

& V_2=\frac{746 \mathrm{~L} \cdot \mathrm{K}}{273 \mathrm{~K}} \\

& V_2 \approx 2.73 \mathrm{~L}

\end{aligned}

$$

And so, the new volume of the gas when increased to 373K will be approximately 2.73L.

## Avogadro’s Law

Amedeo Avogadro made Avogadro’s Law. This was when he was experimenting on the relations between volumes of gases at the same temperature and pressure with an equal number of molecules. Avogadro’s Law was the last among the three laws to be discovered. It also introduced moles in a gas to the relation of pressure, volume, and temperature of a given gas. It enabled more precise calculations. This is because of the link between the macroscopic world of chemical reactions and the microscopic world of individual molecules. Thanks to this addition, many historic fields of chemistry such as stoichiometry were formed with this law as one of its fundamentals.

Avogadro’s Law applies to gases at a constant temperature and pressure. It states that equal volumes of gases contain an equal number of molecules. This law makes a detrimental impact on the different chemical reactions. Avogadro’s Law can be expressed with the formula below:

$$

\frac{V_1}{n_1}=\frac{V_2}{n_2}\\

$$

### Example problem

The temperature and pressure of a gas is kept constant. The sample of gas occupies a volume of 2L at a temperature of 300K and a pressure of 3atm. What will be the new volume of the gas if the number of moles is doubled?

#### Solution

The values that are given are as follows:

V_{1} = 2L

N_{1} = ?

T_{1} = 300K

P_{1} = 3atm

V_{2} = ?

N_{2} = N1*2

T_{2} = 300K

P_{2} = 3atm

Using the values above, we can rearrange the formula to solve for V2 or the new volume of the gas:

$$

\frac{V_1}{n_1}=\frac{V_2}{n_2}\\

\frac{V_1}{n_1}=\frac{V_2}{2 \times n_1}\\

V_2=2 \times V_1\\

V_2=2 \times 2.0 \text { liters }\\

V_2=4.0 \text { liters }\\

$$

So, the new volume of the gas is 4L when the number of moles is doubled at constant temperature and pressure.

In conclusion, knowing the three primary gas laws is very important. These fundamental concepts pave a way into understanding more complex concepts such as the Combined Gas Laws which is the culmination of all the three laws combined to form a new one. The Ideal Gas Law is also another equation that is formed based on the fundamentals of the three primary gas laws. By understanding these laws, we take a step into comprehending the behaviors that govern Gases.

## Frequently asked questions (FAQs)

### Q1 – What is Boyles’s Law?

Boyle’s Law applies to a given gas kept at a constant temperature. The pressure will always be inversely proportional to the volume.

### Q2 – What is Charles’s Law?

Charles’s Law states that the volume of a given gas is directly proportional to its temperature. But this can only be applied at a constant pressure.

### Q3 – What is Avogadro’s Law?

Avogadro’s Law applies to gases at a constant temperature and pressure. It states that equal volumes of gases contain an equal number of molecules.